October 2011 – Women's History and More

Hypatia – A Martyr for the Truth

This was inspired by the life of Hypatia, who lived in the 4^th and 5^th centuries C.E. She was a real person and brilliant mathematician. Often she is the only woman mathematician mentioned in books on the history of math. The character writing is fictitious, but the events are true.

A Day in Alexandria

I arrived in Alexandria as the sun was going down. The trip from Cyrene had been a rough one and I was glad to have my feet on solid ground again. My teacher and mentor, Synesius, had corresponded with her for years. He raved about her brilliance, her inventions, her ability to teach others, and her original mathematical work. Hypatia! Finally, I would hear for myself. Little did I know what horrors I would witness and how the world would change from this year on.

This was my first trip to the great city of Alexandria. I planned to be here for a while to take advantage of the magnificent library (at least what was left of it) and many great teachers. I would eventually find a place to stay, but for now, I had a letter of introduction to a friend of my mentor. He very kindly invited me into his home and gave me a meal and place to sleep for the night. The political climate is very tense these days. It is the year 415 (A.D.) and the Christians are gaining strength in many places. They have very little tolerance for beliefs different from theirs. Cyril, the church patriarch, considers anyone of the neo-Platonic school of thought to be a heretic. But, there are still many of us who are members of this school, including Hypatia.

As we sat down to a simple meal, or rather reclined in the Greek fashion, my host began to tell me a little more about the city and Hypatia.

“You know her!”, I cried.

“Actually, I’m a friend of the family. More her father’s friend.” He replied.

“Please tell me. Are all the stories I hear of her true?”

He laughed, “Actually, many of them are, but what in particular are you interested in knowing?”

“They say she inspires great devotion in her students and anyone interested in learning.”

“She does. She’s a magnificent orator, devoted to teaching, and to the truth. I make sure that I hear her often and read most of what she writes. She has done quite a bit of original work in mathematics, written commentaries and built on the works of some of the greats – Diophantes, Apollonius, among others. ”

“And she is a scientist as well,” I added. “My mentor, Synesius, has been particularly interested in her inventions, such as the astrolabe and the planesphere for studying astronomy.”

“I know nothing of that field, but am told that she has a number of inventions that have added to it. I am more familiar with her writings in mathematics, although, she is very learned in many fields. Her father, Theon, my friend, was determined to produce the ‘perfect human being’ as he says. Many think that he has. Of course, he is a professor of mathematics at the university as well, so he had access to many resources and took charge of her education. I’m sure she picked up the love of mathematical elegance from him, but he didn’t stop there. She learned it all – astronomy, astrology, mathematics, religion. And he didn’t neglect the body. She is accomplished at rowing, swimming, horseback riding . And yes, she is very beautiful as well, even now in her mid 40s. She has also traveled extensively and basically made a name for herself.”

“Did you say she studied religion?”

“Yes, as in ALL religions, rather than one. Theon was particularly concerned that she NOT be caught up in any one religion to the exclusion of new truths. He feels that all dogmatic religions are false. If we can’t be open to new ideas, we have cut ourselves off from the truth. Hypatia has been raised to be very discriminating in her thoughts and acceptance of new ideas. As Theon frequently says, ‘Reserve your right to think, for even to think wrongly is better than not to think at all.’ . . . It hasn’t made it easy for her in the current climate. She is a close personal friend of Orestes, the prefect. I think that is one reason that her popularity is tolerated. But, ever since 412, when Cyril became patriarch, things have become more and more tense. Sometimes I fear for her and others who are seen as champions of other ways of thought.”

“She must be an amazing person. Is she married?”

“She is very beautiful, but no, she has never married. She has had opportunities, but always says that she ‘is married to the truth.’ But, I think you’re a little young for her,” he teased.

I was embarrassed, but still had to ask. “Do you think I could meet her?”

“Hmm . . . I think she has a gathering at her home tomorrow night. Her students often gather there and anyone is welcome. Right now though, it is getting late, and her lecture is the first of the day tomorrow. I had planned to go with you, but won’t be able to if I can’t get any sleep.”

I was the one who had trouble sleeping that night because of my excitement. I was up with the sun and after a brief meal, we set out toward the university. It was a beautiful day as we walked along the bay. The sun was bright and the colors were vivid. It was a perfect complement to what I felt inside. We followed the coast for just a short period before we turned to go up to the main thoroughfare that led to the University of Alexandria. As we approached, it became noisier and more crowded as I expected. When we got closer, however, it seemed to be more of a mob than the usual crowds of a city.

“What is happening?” I asked my new friend.

“I’m not sure. This is unusual. I have friends who live here. Let’s go in and see if we can go up to the roof to get a better view.”

We were allowed entrance by one of the slaves who recognized my host and told us that the master was already on the roof observing. As we joined him, I could see that the street was crowded by an angry mob. In the center of the mob was a woman in her chariot. The crowd had brought the horse to a stop and was attacking the woman, hitting her, grabbing her hair, and throwing stones. I could already see where a clump of her hair had been pulled out. She was fighting back, but it was useless against so many. Someone yelled above the crowd, “to the church, to the altar.” At that point, strong hands grasped the woman and she was carried into the nearby Christian church.

“The poor woman, what can we do? Do you know who she is?”

“That,” whispered my host, “is Hypatia. . . I doubt we can do anything against that mob to help her, but we can try. I know a back way into the church.”

As we raced to the door, fear seized my heart for this woman I had never met, but heard so much about. The mob of people, mostly men, were obvious as Christians by the way that they dressed. I understood that they didn’t favor her teachings, but this anger seemed extreme.

We were unable to get through the door until it was too late. When we did, the extent of their depravity was overwhelming. The mob, whom I later learned was a group of monks from a monastery in the desert, had stripped her and peeled away her skin with bits of tile and pottery. Her limbs had been torn from her body. Her voice was silenced.

I couldn’t stay in Alexandria after that. It wasn’t really safe for a non-Christian foreigner, and besides, I didn’t have the heart for it. I heard rumors later about what had happened. Some said that Hypatia’s limbs were put on display in different parts of the city; some said her body was burned. Orestes fled and Cyril finally had what he wanted – power. I went to Athens to continue study, but everywhere things were changing.

Note: Although partially destroyed in 391 C. E. the library in Alexandria would be completely destroyed a few years after Hypatia’s death and the western world would be plunged into a period that has come to be known as the dark ages.

Carl Sagan speaks about Alexandria and Hypatia:

References

Hubbard, Elbert. Little journeys to the Homes of Great Teachers. Vol.23. New York. The Roycrofters. 1808.

Mlodinow, Leonard. Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace. New York. Simon and Schuster. 2001.

Osen, Lynn. Women in Mathematics. Cambridge, Massachusetts. The MIT Press. 1974.

Women gaining in STEM

I intended this to be a blog about women in history, as in not currently living, but I’ve already added a book review about a women currently fighting for human rights in Afghanistan and I can’t resist posting the link below about the gains women are making in STEM – Science, Technology, Engineering, and Math.

I studied math in college, both undergraduate (in the 70s) and graduate (in the mid 80s.) I remember how few women were in my classes. As a freshman and sophomore there were more, but as those who planned to teach moved on to education classes, there were fewer of us in the more technical classes. (I never really planned to teach high school math, it ended up being a fall back job for me about 20 years later.) When I got to graduate school I studied Applied Math which basically means I was in class with a lot of future engineers. It wasn’t unusual to be one of 4 or 5 women in a class full of men. Oddly enough, we didn’t usually hang out and study together. I guess we just worked on our “boy social dynamics” as Rebecca Allred says in the article. I feel very fortunate that I didn’t really run into any problems. I always had a few classmates to study with which was all I wanted.

Women have made great strides in fields that have traditionally belonged to men. I never really felt as though I had something to prove in those days, but I know many women did. From reading this article it seems as though maybe we really are moving into a time when women can just study and do what they like and are good at without thinking twice about whether it is a man’s field or not. Which is as it should be. Check out the article here.

Women making slow, sure strides in science, math

Malalai Joya – Courage in Afghanistan

A Woman Among Warlords: The Extraordinary Story of an Afghan Who Dared to Raise Her Voice by Malalai Joya

Occasionally I’ll post book reviews from Goodreads when they are about women who I think are worth noting. Malalai Joya certainly falls in that category.

First off let me say, there have been 2 versions of this book released. I just bought it for my Kindle last week, so I have the latest edition. I did not find the writing as objectionable as some reviewers have. I’m sure as in most books there are areas where it could be improved, but it was not a distraction to me at all.

There are many extraordinary men and women in this world and this book is the story of one of them. Although Malalai Joya is a young woman, she has an important story to tell. Born into war-torn Afghanistan, she was fortunate to have a father who was educated and wanted his children to be educated as well – an estimated 80% of Afghan women are illiterate. Her father also instilled in her a love of democracy.

Malalai Joya is not her real name, but it is the name she goes by in most areas of her life in order to protect her family. Born in 1978, she has never known a time when her country was not at war. In A Woman Among Warlords, Joya describes her life in rural Afghanistan, refugee camps in both Iran and Pakistan, teaching in underground schools for girls, and finally being elected to the new Parliament only to be ejected for speaking out. Her life is constantly in danger, and although she has traveled outside of Afghanistan to speak and carry her message, she won’t consider staying out of the country. Love for the real Afghanistan, the people, comes through on every page.

The book gives a brief history of Afghanistan to fill in background for the current struggle. She speaks knowledgeably about the roles other governments have played in this history and credits the research team who helped her gather this information. I have read several other books about Afghanistan and the facts are consistent with what I’ve read.

Although the book carries a message of hope, it is not a feel good book. She conveys a picture of the horrors that the Afghan people have had to endure and is critical of the people who have brought it about. This includes both Afghans such as the warlords and the president Hamid Karzai, but also the former Soviet Union and the current US/NATO occupation. However, just as she is able to distinguish between the Afghan government and the people of Afghanistan, she distinguishes between the people of western countries and their governments. Joya is thankful for being able to carry her message to Europe and the US, and for the help she has received from some western organizations.

The message could sound hopeless, but she doesn’t see it that way. In the last chapter Joya gives suggestions to people who want to help. As an American, I have often wondered how we could leave Afghanistan with so many problems, many of which we caused, knowing that there are so many warring factions. Joya is insistent that, if democracy is to be attained in Afghanistan, it will be because the people secure it for themselves. The message I get from this book is that yes they would like our help, but from a distance.

Maria Gaetana Agnesi – 18th century mathematician

Maria Gaetana Agnesi, artist unknown (source)

“How long will I have to do this?” must have been the thought that frequently ran through the mind of Maria Agnesi as she stood in her parlor on Friday nights. Maria Gaetana Agnesi was the oldest of 21 children born into the family of Pietro Angesi. The Agnesi family was a well to do family in Milan, Italy in the 18^th century. Pietro came from a merchant class family who had made their money in cloth goods. The family owned many properties and had furnished them exquisitely.

Pietro’s grandfather, father, and uncle had built the business into a sort of empire. For some unknown reason, Pietro was never trusted with the business. Even when his father died, provision was made in his will that prevented him from making any decisions concerning the business without the approval of his uncle. However, when his uncle died childless, the responsibility for the business fell entirely onto Pietro’s shoulders.

Pietro was a very ambitious man. He had almost everything that he could want, materially. The one thing he didn’t have was a position in the aristocracy. He tried many things to be recognized as a member of this class which eventually ran up a huge debt. One of these things was hosting “conversazione” on Friday nights. There were many such events held around the city for the wealthy to indulge themselves. Some were for music and dancing, some for gambling, but at the Agnesi household discussions of philosophy were held. These events served their purpose and attracted many distinguished persons to the Agnesi home such as Monsieur Charles Brosses, president of the parliament of Burgundy and Frederick Christian, heir to the throne of Poland.

One thing Pietro never scrimped on, even when he was accumulating debt, was his children’s education. He hired the best tutors from around Europe for both the boys and the girls. This was during a time when women across Europe were rarely educated. Genius was, however, recognized and Maria Gaetana was that – a child prodigy. By the age of 11, she could speak, read, and write Italian, French, German, Spanish, Latin, Greek, and Hebrew. At the age of 9, she translated a treatise written in Italian into Latin, memorized it, and delivered the oration at one of her father’s “conversations”. The treatise was on the education of women, arguing that they should be allowed access to “the fine arts and sublime sciences”.

She and her sister were regularly put on display in the salon of their family home. Here her father entertained many wealthy and noble men. Maria Gaetana was asked questions by the participants and she would expound on the subject. She was adept at discussing philosophy as well as the sciences and mathematics. She was brilliant, and the men who attended were amazed that she could discuss the philosophy of Descartes as easily as celestial mechanics or the theory of gravitation. Her sister, Maria Teresa, was a composer. She would play the harpsichord and sing, sometimes accompanied by Maria Gaetana on the viola.

Maria Gaetana (1718 – 1799) was basically shy and reserved person. She didn’t enjoy being put on display, but was obedient to her father’s wishes. A devout Catholic, at one point during her teens, she approached him to ask if she could be excused from further events. She wanted to enter the cloister. Her father refused to allow this and she continued participating. Maria Gaetana never married and most of her time was spent teaching the younger children and after her mother (Anna Brivio) died in 1732, managing the household. What time she could spare, she gave in helping ill and homeless people, primarily women.

First page of "Analitical Institutions", 1748 (source) — First page of “Analytical Institutions”, 1748 (source)

As she got older, one of Maria Gaetana’s responsibilities was to tutor her younger brothers in mathematics. She had a passion for scholarship including mathematics and had absorbed works by Newton, Fermat, and Descartes among others. She found all of the texts available to be inadequate for the task of teaching her younger siblings. For this reason she decided to write her own. Originally, it was intended to be used only for their lessons but 10 years after she began it, Analytical Institutions was published to wide acclaim. It was a comprehensive look at mathematical analysis at the time, from algebra through differential and integral calculus, infinite series, and differential equations. She managed to synthesize work from many of the masters including Newton and Leibnitz to write a text that made these topics accessible to the lay person.

Maria had previously published Propositiones Philosophicae a volume of about 200 essays on various topics presented at her father’s conversations. But she is primarily known for Analytical Institutions. It is the earliest surviving math text written by a woman and was translated into English and French for use as a textbook. She was honored by such people as Pope Benedict XIV with a gold medal and Empress Maria Theresa with jewels. She was also elected to the Bologna Academy of Sciences. This position included a faculty post. There is some disagreement as to whether or not she ever taught there.

Whether or not Maria Gaetana taught outside the home, this would have ended when her father died in 1752. He had left the family in tremendous debt and most of their possessions had to be sold to cover it. This changed Maria’s lifestyle and set her free to pursue her passion. Until her death in 1799, Maria Gaetana gave selflessly to others. She worked with the ill and homeless people of Milan with both her time and what resources she had left.

The "Witch of Agnesi" curve (source) — The “Witch of Agnesi” curve (source)

Maria Gaetana Agnesi is most well known for a curve that she worked with called the “Witch of Agnesi.” Known for, that is, outside of Italy. In Italy she is known as a great humanitarian and woman of God. She was buried in a common grave with 15 other women and her childhood home was destroyed during WWII. But the city of Milan is proud of their daughter and there are monuments that have been erected to celebrate her life.

Bust of Maria Gaetana Agnesi, beneath the arcades of the courtyard of the Palace of Brera at Milan. Photographer: Giovanni Dall'Orto (source) — Bust of Maria Gaetana Agnesi, beneath the arcades of the courtyard of the Palace of Brera at Milan. Photographer: Giovanni Dall’Orto (source)

References
The World of Maria Gaetana Agnesi, Mathematician of God
by Massimo Mazzotti
Women in Mathematics by Lynn Osen

Read about other Famous Women Mathematicians and Scientists